Question

Points A(-2, 4), B(1, 3), C(4, -1) and D form a parallelogram. What are the coordinates of D?

(5, 5)



(0, 0)



(1, -2)



(1, 0)



(3, 4)

Answer 1

After some work I concluded that the coordinates to D are (-2,0) 

Answer 2

Answer: The coordinates of D are (1,0).

Explanation:

Given : The vertices of parallelogram are A(-2, 4), B(1, 3), C(4, -1) and D.

Let the fourth vertex be D(x,y).

We know that the diagonal of parallelogram bisects each other.

i.e. Mid points of AC = Mid point of BD [ where AC and BD are diagonals of parallelogram ]

i.e.

`((-2+4)/(2),(4-1)/(2))=((1+x)/(2),(3+y)/(2))\\\\\Rightarrow\ (1,(3)/(2))=((1+x)/(2),(3+y)/(2))\\\\\Rightarrow\ (1+x)/(2)=1\ \ \ \ , \ (3+y)/(2)=(3)/(2)\\\\\Rightarrow\ 1+x=2\ ,\ \ \ 3+y=3\\\\\Rightarropw\ x=1\ \ ,\ \ y=0`

Hence, the coordinates of D are (1,0).